N.QN  CIRCULATING 

CHECK  FOR  UNBOUND 
CIRCULATING  COPY 


UNIVERSITY  OF  ILLINOIS 

Agricultural  Experiment  Station 


BULLETIN  No.  263 


RELATION  OF  SOLIDS  IN  MILK  TO  FAT 
AND  SPECIFIC  GRAVITY  OF  THE  MILK 

BY  0.  R.  OVERMAN,  F.  A.  DAVIDSON,  AND  F.  P.  SANMANN 


URBANA,  ILLINOIS,  APRIL,  1925 


RELATION  OF  SOLIDS  IN  MILK  TO  FAT 
AND  SPECIFIC  GRAVITY  OF  THE  MILK 

By  O.  R.  OVERMAN,  Assistant  Chief  in  Dairy  Chemistry,  F.  A.  DAVIDSON,  First 

Assistant  in  Dairy  Husbandry,  and  F.  P.  SANMANN,  Instructor  in 

Dairy  Chemistry  in  the  College  of  Agriculture 

The  use  of  formulas  for  computing  the  percentage  of  total  solids  or 
of  solids-not-fat  in  milk  has  been  common  both  in  the  United  States  and 
in  Europe  for  many  years.  These  formulas  are  based  upon  the  specific 
gravity  and  the  percentage  of  fat  in  the  milk. 

The  idea  that  a  relation  exists  between  specific  gravity,  fat,  and 
solids  in  milk  seems  to  have  occurred  first  to  Behrend  and  Morgen.1 
Clausnizer  and  Mayer,2  and  HehnerJ>  published  formulas  in  the  attempt 
to  show  this  relation.  These  formulas  were  based  on  inaccurate  data 
and  have  been  abandoned. 

Fleischmann  and  Morgen4  published  a  formula  which  was  later 

corrected  by  Fleischmann.5    This  formula  is  T  =  .2665  

S 

-f-  1.2  F,  in  which  T  =  percentage  of  total  solids,  S  =  specific  gravity 
of  milk  at  15°  C.,  and  F  =  percentage  of  fat  in  milk.       Q 

Richmond0  has  developed  the  formula  T  =  .262  —  -f-   1.2  F,  in 

which  G  =  Quevenne  lactometer  reading,  D  =  specific  gravity,  and 
F  =  percentage    of    fat,    and   has    found    that   the    simpler    formula 

C^  f 

T= 1 F-J--14  gives  results  which  correspond  very  closely  with 

4         5 
it  if  the  specific  gravity  is  between  1.020  and  1.036.    This  formula  is 

commonly  used  in  England. 

Babcock7  published  the  formula  total  solids  = 1-  f,  in 

3.8 
which  L  =  Quevenne  lactometer  reading  and  f  =  percentage  of  fat. 

Babcock8  later  stated  this  relation  as  total  solids  =  -•  +  1.2  F.  With 

the  addition  of  .14  this  is  the  same  as  Richmond's  formula. 

This  formula  of  Babcock  is  most  commonly  used  in  the  United 
States  and  for  that  reason  was  selected  for  making  all  computations  of 
total  solids  which  are  recorded  in  this  bulletin.  Babcock's  formula  for 

solids-not-fat  as  used  at  the  present  time  is  S.N.F.  = f-  .2  F  -f-  .14. 

4 

The  purpose  of  this  investigation  was  to  show,  by  means  of  a  statis- 
tical analysis,  the  relation  existing  between  the  percentages  of  total 
solids  as  determined  by  weight  (A.O.A.C.  method)  and  the  correspond- 

263 


264  BULLETIN  No.  263  [April, 

ing  percentages   of  total   solids   as  computed   by   the   formula  T.S.  = 

[-1.2  F  when  applied  to  a  large  number  of  milk  samples;  also  the 

4 
effect  upon  the  results  of  the  size  of  the  lot  of  milk  sampled.  The  relation 

between  the  percentages  of  solids-not-fat  as  determined  by  difference 
and  the  corresponding  percentages  of  solids-not-fat  as  computed  by  the 

formula  S.N.F.  = \-  .2  F  also  was  studied. 

PLAN  OF  INVESTIGATION 
SOURCE  OF  MILK  SAMPLES 

This  investigation  involved  a  statistical  study  of  the  percentages  of 
total  solids  and  of  solids-not-fat  by  weight,  and  the  corresponding  per- 
centages of  total  solids  and  of  solids-not-fat  by  formula,  as  determined 
from  three  different  groups  of  milk  samples,  namely: 

(1)  1158  Samples  from  Individual  Cows. — Most  of  these  samples 
were  composites  of  the  milk  produced  during  three-day  periods  selected 
at   regular   intervals    thruout   the   lactations    of   the   cows.-    A   few    of 
these  samples  represent  only  one  milking.    The  cows  used  were  all  in 
the  dairy  herds  at  the  University  of  Illinois  and  represent  the  Ayrshire, 
Guernsey,  Holstein  and  Jersey  breeds,  and  Guernsey-Holstein  crosses. 

(2)  134  Random  Samples  of  Mixed  Milk. — These  samples  were 
taken  from  cans  of  milk  delivered  at  milk  plants,  from  weigh-tanks,  and 
from  storage  and  pasteurizing  vats.   No  record  was  kept  of  the  sizes  of 
the  lots  of  milk  from  which  the  samples  were  taken;  they  varied,  how- 
ever, from  less  than  10  gallons  to  150  gallons  or  more. 

(3)  40  Samples  Taken  from  Large  Lots  of  Milk. — These  samples 
were  all  taken  from  storage  or  pasteurizing  vats  in  plants  which  handle 
milk  in  large  quantities.    Records  were  kept  of  the  sizes  of  these  lots, 
which  varied  from  135  gallons  to  3,000  gallons. 

In  every  case  care  was  taken  to  make  certain  that  the  sample  ob- 
tained was  representative  of  the  lot  of  milk  from  which  it  was  secured. 

CHEMICAL  ANALYSIS 

All  samples  were  put  into  glass  jars  and  securely  sealed  to  prevent 
evaporation  of  the  water  from  the  samples.  The  samples  were  also  pre- 
served with  formaldehyde  in  approximately  the  quantity  recommended 
by  Palmer.9 

Determinations  were  made  of  specific  gravity,  percentage  of  fat, 
ancf  percentage  of  total  solids. 

The  specific  gravity  was  obtained  at  15.5°  C.  with  a  chainomatic 
specific-gravity  balance.  At  least  two  adjustments  and  readings  of  the 
vernier  scale  on  the  balance  were  made  in  determining  the  specific 
gravity  of  each  sample. 


1925]  MILK.  SOLIDS,  FAT,  AND  SPECIFIC  GRAVITY  265 


percentage  of  fat  was  determined  by  the  Roese-Gottlieb 
method,  about  5  grams  of  milk  being  weighed  into  a  Rohrig  tube.  The 
volumes  of  reagents  used  were  reduced  from  those  given  in  the  methods 
of  analysis10  of  the  A.O.A.C.  to  correspond  to  the  weight  of  milk  used. 
Duplicate  determinations  were  made  in  each  case  and  the  average  of 
the  duplicates  reported  as  the  percentage  determined. 

The  percentage  of  total  solids  was  determined  by  weighing  2  to  3 
grams  of  the  sample  into  a  weighed  flat  bottom  lead  dish  and  heating 
to  constant  weight  at  the  temperature  of  boiling  water.  Duplicate  deter- 
minations were  made  and  the  average  of  the  duplicates  reported  as  the 
percentage  determined. 

The  percentage  of  solids-not-fat  was  determined  by  subtracting  the 
percentage  of  fat  by  weight  from  the  percentage  of  total  solids  by 
weight.  To  avoid  confusion,  this  percentage  of  solids-not-fat  will  be 
spoken  of  as  percentage  of  solids-not-fat  by  weight. 

STATISTICAL  ANALYSIS 

The  percentage  of  total  solids  was  computed  from  the  specific 
gravity  and  percentage  fat  content  of  each  sample  according  to  the 

formula  T.S.  =  --  1-  1.2  F.    The  percentage  of  total  solids  by  weight 

4 
for  each  sample  was  subtracted  algebraically  from  its  corresponding 

percentage  of  total  solids  by  formula.  In  this  way  1,158  differences 
were  determined  for  the  first  group  of  samples,  134  differences  for  the 
second  group,  and  40  differences  for  the  third  group.3 

The  me<m  and  the  standard  deviation  of  the  differences  for  each 
group  of  samples  were  determined.  A  comparison  was  then  made  be- 
tween the  means  of  the  differences  of  the  respective  groups  of  samples 
and  likewise  between  the  standard  deviations. 

The  mean  of  the  differences  of  each  group  of  samples  ±2.14b  times 
the  corresponding  standard  deviation  of  the  differences  gave  limits  such 
that  the  chances  are  30:1  that  any  single  difference  determined  by  the 
above  methods  for  that  group  of  samples  will  fall  within  them. 

RESULTS 

The  results  from  the  chemical  and  statistical  analysis  of  the  three 
groups  of  samples  include  the  percentage  of  fat,  the  percentage  of  total 

*The  percentage  of  solids-not-fat  was  computed  from  the  specific  gravity  and  the 

L 
percentage  of  fat  of  each  sample  according  to  the  formula  S.N.F.  =  --  (-  .2  F.  The 

4 
percentage  of   solids-not-fat   by  weight   for  each   sample  was   subtracted   algebraically 

from  its  corresponding  percentage  of  solids-not-fat  by  formula.  These  differences  are 
identical  with  the  differences  between  the  total  solids  by  weight  and  by  formula  for  the 
same  samples. 

bDetermined  from  the  equation  given  on  page  xviii  of  Karl  Pearson's  Tables  for 
Statisticians. 


266 


BULLETIN  No.  263 


[Apr*, 


solids  by  weight,  the  percentage  of  solids-not-fat  by  weight,  the  per- 
centage oT  total  solids  by  formula,  the~percentage  of  ^olids-not-fat  by 
formula,  the  specific"  gravity  at  15.5°  C.,  and  also  the  algebraic-differ- 
ences determined  by  subtracting  the  percentages  of  total  solids  by  weight 
from  their  corresponding  percentages  of  total  solids  by  formula.  The 
differences  for  the  solids-not-fat  are  identical  with  the  corresponding 
differences  for  the  total  solids.  These  differences  are  shown  graphically 


Vat 


\ 


+/.C*S*.f-fS  *.f+S  +.-**S  *.*IS  f.0*f  -./fS  -.JSS  -Aff  -.7SS   -.*fS  -/./SS  -/.JSS 

J>i/S*rences    (Cta-ss  Jnid -Points ) 

FIG.    1. — FREQUENCY   DISTRIBUTION   OF   THE   DIFFERENCES   BE- 
TWEEN TOTAL  SOLIDS  AND  SOLIDS-NOT-FAT  FOR  THREE  GROUPS 
OF  SAMPLES:    INDIVIDUAL,  RANDOM,  AND  VAT 

in  Fig.  1.  Table  1  includes  the  mean,  the  standard  deviation,  and  the 
limits  at  odds  of  30:1  of  the  differences  determined  for  each  group  of 
samples. 

Themeanof  the  differences3  for  thefirst  groupof  samples  (samples  of 
milk  from  individual  cows)  is  —  .173  percent.  In  other  words,  the  percent- 

"Differences  between  the  percentages  of  total  solids  by  weight  and  the  correspond- 

L 

ing  percentages  of  total  solids  by  the  formula  T.S.  = 1-  1.2  F. 

4 


19251 


MILK  SOLIDS,  FAT,  AND  SPECIFIC  GRAVITY 


267 


ages  of  total  solids  determined  by  weight  for  samples  of  milk  from  individ- 
ual cows  are  on  the  average  .173  percent  greater  than  the  percentages  of 

total  solids  computed  for  the  same  samples  by  the  formula  T.S.  =  — 

-f-  1.2  F.  The  mean  of  the  differences  for  the  second  group  of  samples 
(random  samples  from  milk  of  more  than  one  cow)  is  — .105  percent. 
The  mean  of  the  differences  for  the  third  group  of  samples  (samples 
from  large  vats  of  milk)  is  also  —  .105  percent.  Hence,  the  percentages 
of  total  solids  determined  by  weight  in  milk  from  two  or  more  cows  and 
in  milk  from  many  cows,  are  on  the  average  .105  percent  greater  than 
their  corresponding  percentages  of  total  solids  computed  by  the  formula 

T.S.  =  —  +  1.2  F. 
4 

TABLE  1. — MEANS  AND  STANDARD  DEVIATIONS  OF  DIFFERENCES  BETWEEN 
SOLIDS  BY  WEIGHT  AND  SOLIDS  BY  FORMULA 


Samples 

Number  of 
differences 

Mean 
percentage 

Standard 
deviation, 
percent 

Limits  at  odds 
of 
30:1  percent 

Individual  

1158 

—  1  73  -+-  0067 

340-*-  0048 

—.173  ±.727 
or 

+.554  and  —.900 

Random  

134 

—  105  •+•  0014 

242-*-  0010 

—  .105±.519 
or 

+.414  and  —.624 

Vat  

40 

—  105  -1-  0011 

10Q-+-  0008 

—  .105±.214 
or 

+.109  and  —.319 

Altho  the  means  of  the  differences  for  the  three  types  of  samples 
differ  very  little  from  each  other,  it  does  not  follow  that  the  formula  is 
equally  as  accurate  in  computing  the  percentages  of  total  solids  within 
them,  as  will  be  shown  later  on. 

The  standard  deviation  of  the  differences  for  the  three  groups  of 
samples  are  .340,  .242,  and  .100  percent  respectively.  The  standard 
^deviation  is  a  'measure  of  variability;  hence,  as  the  number  of  cows 
contributing  to  the  milk  samples  is  increased,  the  variability  in  the 
differences  between  the  percentages  of  total  solids  by  weight  and  their 
corresponding  percentages  of  total  solids  by  formula,  is  markedly  de- 
creased. This  relation  is  illustrated  very  clearly  in  Fig.  1,  wherein  the 
differences  for  each  group  of  samples  are  shown  graphically.  In  Fig.  1 
it  will  be  found  that  the  differences  for  the  first  group  of  samples  range 
from  -f- 1.045  to  —1.355  percent,  for  the  second  group  of  samples  from 
-(-.845  to  — .555  percent,  and  for  the  third  group  of  samples  from 
-J-.145  to  —.255  percent. 


268  BULLETIN  No.  263  [April, 

Putting  this  variability  into  practical  terms  we  have  in  Table  1 
limits  such  that  the  odds,  or  chances,  are  30:1  that  any  single  difference 
determined  by  the  above  methods  for  each  group  of  samples  will  fall 
within  them.  The  limits  for  the  first  group  of  samples  are  -(-.554  and 
— .900  percent;  i.  e.,  for  samples  from  individual  cows  the  chances  are 

30:1  that  the  percentages  of  total  solids  by  the  formula  (T.S.  =  — 

+  1.2  F)  will  lie  within  +.554  and  —.900  percent  of  their  correspond- 
ing percentages  of  total  solids  by  weight. 

The  limits  at  odds  of  30:1  for  the  second  group  of  samples  are 
+.414  and  — .624  percent,  and  for  the  third  group  of  samples  +.109 
and  — .319  percent.  Hence,  as  the  number  of  cows  contributing  to  the 
samples  of  milk  are  increased  the  limits  are  decreased  within  which  the 
chances  are  30:1  that  the  percentage  of  total  solids  computed  by  the 
above  formula  will  deviate  from  its  corresponding  percentage  of  total 
solids  by  weight.  L 

If  the  formula  (T.S.  = 1-  1.2  F)  be  corrected  for  samples  of 

4 
milk  from  individual  cows  by  adding  the  mean  of  the  above  differences 

for  these  samples,  it  will  read  T.S.  = 1-  1.2  F  +.173.     In  accord- 

4 
ance  with  this  formula  the  limits  at  odds  of  30:1  will  also  be  corrected 

to  ±.727  percent.  The  limits  of  ±.727  percent  were  determined  by 
adding  .173  percent  to  the  above  limits  of  +.554  and  —.900  percent. 

In  like  manner  the  formula  T.S.  = \-  1.2  F  will  be  corrected  for  the 

4  L 

second  and  third  groups  of  samples  to  read  T.S.  = 1-  1.2  F  +  .105. 

4 
Altho  the  corrected  formulas  for  the  second  and  third  groups  of  samples 

are  the  same,  the  limits  at  odds  of  30:1  are  much  different  and  will  be 
±.519  percent  and  ±.214  percent  respectively.  Hence,  it  can  readily 
be  seen  that  the  standard  deviation  or  variability  within  the  above  dif- 
ferences determines  the  accuracy  of  the  formula  T.S.  = 1-  1.2  F  in" 

computing  the  percentages  of  total  solids  in  milk  from  the  respective 
sources.  The  mean  of  the  above  differences  has  a  bearing  on  the  accu- 
racy of  the  formula  when  combined  with  the  standard  deviation,  but 
without  the  latter  it  has  very  little  meaning. 

The  probable  errors  of  the  means  and  the  standard  deviations  of 
the  differences  as  reported  in  Table  1  are  all  many  times  less  than  their 
constants.  Hence,  it  may  safely  be  assumed  that  the  samples  from  which 
these  constants  were  derived  are  representative  of  the  general  popula- 
tions of  samples  of  the  respective  types. 

As  the  differences  between  the  percentages  of  solids-not-fat  by 
weight  and  of  solids-not-fat  by  formula  are  identical  with  the  corre- 


1925]  MILK.  SOLIDS,  FAT,  AND  SPECIFIC  GRAVITY  269 

spending  differences  for  the  total  solids,  the  means,  standard  deviations, 
and  limits  at  odds  of  30:1  are  the  same.  T 

The  formula  for  solids-not-fat  (S.N.F.  = 1-  .2  F)  corrected  for 

.  4  L 

samples    of    milk    from    individual    cows    will    read    S.N.F.  — f- 

4 

.2  F  -f-  .173;  for  the  second  and  third  groups  it  will  read  S.N.F.  = (- 

.2  F  +  .105. 

SUMMARY 

The  formula  T.S.  = 1-  1.2  F  -{-.173  in  computing  the  percent- 
age of  T.S.  in  milk  from  individual  cows  is  accurate  in  so  far  as  the 
chances  are  30:1  that  the  percentages  of  total  solids  computed  by  it 
will  lie  within  ±.727  percent  of  their  corresponding  percentages  of  total 
solids  by  weight.  In  other  words,  it  may  be  expected  that,  on  the  average, 
the  percentages  of  total  solids  by  the  above  formula  for  30  samples  out 
of  every  31  samples  will  lie  within  ±.727  percent  of  their  correspond- 
ing percentages  of  total  solids  by  weight.  Likewise,  the  percentage  of 
total  solids  by  the  above  formula  for  one  sample  out  of  every  3 1  samples 
will  lie  without  the  range  of  ±.727  percent  of  its  corresponding  per- 
centage of  total  solids  by  weight. 

The  formula  T.S.  = \-l.2F-\-  .105  in  computing  the  percent- 

4 
age  of  total  solids  in  random  samples  of  milk  from  two  or  more  cows  is 

accurate  in  so  far  as  the  chances  are  30:1  that  the  percentages  of  total 
solids  computed  by  it  will  lie  within  ±.519  percent  of  their  correspond- 
ing percentages  of  total  solids  by  weight.  Hence,  it  may  be  expected 
that  on  the  average  the  percentages  of  total  solids  computed  by  the 
above  formula  for  30  samples  out  of  every  31  samples  will  lie  within 
the  range  of  ±.519  percent  of  their  corresponding  percentages  of  total 
solids  by  weight.  Likewise,  the  percentage  of  total  solids  by  the  above 
formula  for  one  sample  out  of  every  31  samples  will  lie  without  the 
range  of  ±.519  percent  of  its  corresponding  percentage  of  total  solids 
by  weight.  T 

The  formula  T.S.  = \-  1.2  F  -|-  .105  may  also  be  used  in  com- 
puting the  percentage  of  total  solids  in  milk  from  large  vats  and  storage 
tanks,  i.  e.,  milk  from  many  cows.  In  using  this  formula  to  compute  the 
percentage  of  total  solids  in  such  milk,  it  may  be  expected  that  on  the 
average  the  percentages  of  total  solids  computed  by  it  in  30  samples 
out  of  every  31  samples  will  lie  within  ±.214  percent  of  their  corre- 
sponding percentages  of  total  solids  by  weight.  In  like  manner  the  per- 
centage of  total  solids  by  the  formula  for  one  sample  out  of  every  31 
samples  will  lie  without  the  range  of  ±.214  percent. 

The  formula  S.N.F.  =  —  -|- .2  F  +.173   in  computing  the  per- 
4 


270  BULLETIN  No.  263  {April, 

centage  of  solids-not-fat  in  the  milk  from  individual  cows  is  accurate 
in  so  far  as  the  chances  are  30:1  that  the  percentages  of  solids-not-fat 
computed  by  it  will  lie  within  ±.727  percent  of  their  corresponding 
percentages  of  solids-not-fat  by  weight. 

L 

The  formula  S.N.F.  = \-  2  F  -f-  .105  may  be  used  to  compute 

4 
the  percentage  of  solids-not-fat  in  the  mixed  milk  from  two  or  more 

cows.  For  such  samples,  taken  at  random,  the  chances  are  30:1  that  the 
percentages  of  solids-not-fat  computed  by  it  will  lie  within  ±.514  per- 
cent of  their  corresponding  percentages  of  solids-not-fat  by  weight.  For 
samples  taken  from  large  vats  and  storage  tanks,  the  chances  are  30:1 
that  the  computed  percentages  of  solids-not-fat  will  lie  within  ±.214 
percent  of  their  corresponding  percentages  of  solids-not-fat  by  weight. 


CONCLUSIONS 

1.  The  accuracy  of  the  formula  T.S.  = \-  1.2  F  in  computing 

4 
the  percentage  of  total  solids  in  milk  increases  as  the  number  of  cows 

contributing  to  the  milk  is  increased. 

2.  The  formula  T.S.  = 1-  1.2  F  -(-.173  may  be  used  in  com- 
puting the  percentage  of  total  solids  in  milk  from  individual  cows,  but 
the  variability  within  the  results  is  too  great  to  make  it  of  any  prac- 
tical use. 

3.  The  formula  T.S.  = (-  1.2  F  -f-  .105  when  used  to  compute 

4 
the  percentage  of  total  solids  in  milk  from  many  cows  gives   results 

which  very  closely  approximate  those  determined  by  direct  chemical 
analysis,  and  in  plants  handling  large  quantities  of  milk  may  be  used 
with  relative  satisfaction.  y 

4.  The  accuracy  of  the  formula  S.N.F.  =  —  -\-  .2  F  in  comput- 
ing the  percentage  of  solids-not-fat  in  milk  increases  as  the  number  of 
cows  contributing  to  the  milk  is  increased. 

5.  The  formula  S.N.F.  = \-  .2  F  -f  .173  may  be  used  in  com- 

4 
puting  the  percentage  of  solids-not-fat  in  milk  from  individual  cows,  but 

the  variability  within  the  results  is  too  great  to  make  it  of  any  prac- 
tical use.  j 

6.  The  formula  S.N.F.  = (-  .2  F  -j-  .105  may  be  used  in  com- 

4 
puting  the  percentage  of  solids-not-fat  in  large  lots  of  milk.   The  results 

obtained  approximate  closely  enough  to  those  obtained  by  chemical 
analysis  to  be  of  practical  value. 


1925]  MILK  SOLIDS,  FAT,  AND  SPECIFIC  GRAVITY  271 

LITERATURE  CITED 

1.  BEHREND,  PAUL,  AND  MORGEN,  AUGUST 

Ueber  die  Bestimmung  der  Trockensubstanz  in  der  Milch  nach  dem  specifischen 
Gewicht  derselben.  Jour.  Landw.  27,  249-259.  1879. 

2.  CLAUSNIZER,  F.,  AND  MAYER,  ADOLF 

Forschungen  auf  dem  Gebiete  der  Viehhaltung.  6,  265,  1879.  Thru  Tour 
Landw.  30,  293.  1882. 

3.  HEHNER,  OTTO 

On  the  relation  between  the  specific  gravity,  the  fat,  and  the  solids-not-fat  in 
milk.  Analyst,  7,  129-133.  1882. 

4.  FLEISCHMANN,  WILHELM,  AND  MORGEN,  AUGUST 

Ueber  die  Beziehungen  welche  zwischen  dem  specifischen  Gewicht  der  Milch 
einerseits  und  dem  procentischen  Gehalt  derselben  an  Fett  und  Trock- 
ensubstanz andrerseits  bestehen.  Jour.  Landw.  30,  293-309.  1882. 

5.  FLEISCHMANN,  WILHELM 

Beitrage  zur  Kenntnis  des  Wesens  der  Milch.   Jour.  Landw.   33,  251-267.    1885. 

6.  RICHMOND,  H.  D. 

Dairy  Chemistry,  84-89.    1920. 

7.  

The  relation  between  specific  gravity,  fat,  and  solids-not-fat  in  milk.  Analyst 
20,  57-58.  1895. 

8.  BABCOCK,  S.  M. 

The  estimation  of  the  total  solids  in  milk  from  the  percent  of  fat  and  the  specific 
gravity  of  the  milk.  Wis.  Agr.  Exp.  Sta.,  Ann.  Rpt.,  1891,  292-307. 
1892. 

9.  FARRINGTON,  E.  H. 

Report  on  dairy  products.  U.  S.  Dept.  of  Agr.,  Div.  of  Chem.,  Bui.  47,  122- 
125.  1894. 

10.  PALMER,  L.  S. 

The  preservation  of  milk  for  chemical  analysis.  Mo.  Agr.  Exp.  Sta.,  Res.  Bui. 
34,  29.  1919. 

11.  ASSOCIATION  OF  OFFICIAL  AGRICULTURAL  CHEMISTS 

Official  and  tentative  methods  of  analysis  adopted  by  the  Association  of  Official 
Agricultural  Chemists,  227.  1920. 

ACKNOWLEDGEMENT 

The  authors  wish  to  express  their  appreciation  of  the  courtesy  shown  them  by  the 
companies  named  below.  The  random  samples  and  the  samples  from  large  lots  of  milk 
were  for  the  most  part  obtained  in  plants  operated  by  these  companies:  Blue  Banner 
Dairy  Company,  Danville;  Borden  Farm  Products  Company,  Chicago;  Bredehoft 
Dairy  Company,  Danville;  Champaign  Sanitary  Milk  Company,  Champaign;  Horne- 
man-Cossey  Company,  Danville;  Illinois  Dairy  Company,  Springfield;  Snow  and  Palmer, 
Bloomington;  Wieland  Dairy  Company,  Chicago. 


UNIVERSITY  OF  ILLINOIS-URBAN* 


